A&A 418, 283-294 (2004)

DOI: 10.1051/0004-6361:20035619

## Evolutionary sequences of rotating protoneutron stars

**L. Villain**

^{1, 2, 3}, J. A. Pons^{1, 4}, P. Cerdá-Durán^{1}and E. Gourgoulhon^{3}^{1}Departament d'Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain,

^{2}Copernicus Astronomical Center (CAMK), Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland

^{3}Laboratoire de l'Univers et de ses Théories, UMR 8102 du CNRS, Observatoire de Paris - Section de Meudon, 92195 Meudon Cedex, France

^{4}Departament de Física Aplicada, Universitat d'Alacant, Apartat de correus 99, 03080 Alacant, Spain

(Received 3 November 2003 / Accepted 19 January 2004 )

** Abstract **

We investigate the evolution of rigidly and differentially rotating
protoneutron stars during the first twenty seconds of their life.
We solve the equations describing stationary axisymmetric configurations
in general relativity coupled to
a finite temperature, relativistic equation of state, to obtain a sequence
of quasi-equilibrium configurations describing the evolution of newly
born neutron stars.
The initial rotation profiles have been taken to mimic the situation
found immediately following the gravitational collapse of rotating
stellar cores. By analyzing the output of several models, we estimate that
the scale of variation of the angular velocity in a newly born neutron star
is of the order of 7-10 km. We obtain the maximum rotation frequency
that can be reached as the protoneutron stars
deleptonizes and cools down, as well as other relevant parameters such as
total angular momentum or the instability parameter
|*T*/*W*|.
Our study shows that imposing physical constraints (conservation of baryonic mass
and angular momentum) and choosing reasonable
thermodynamical profiles as the star evolves gives results
consistent with the energetics of more complex simulations of non-rotating
protoneutron stars. It appears to be unlikely that
newly born protoneutron stars formed in nearly axisymmetric core collapses
reach the critical angular velocity to undergo the bar mode instability.
They could, however, undergo secular or low
|*T*/*W*| rotational instabilities
a few seconds after birth, resulting in a strong emission of gravitational
waves retarded with respect to the neutrino luminosity peak.
We also found that the geometry of strongly differentially rotating protoneutron stars
can become toroidal-like for large values of the angular velocity, before reaching
the mass shedding limit.

**Key words:**stars: neutron

**--**stars: rotation

**--**stars: evolution

Offprint request: L. Villain, loic@camk.edu.pl

**©**

*ESO 2004*